# Math: Algebra

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Landon can climb a certain hill at a rate that is 2.5 mph slower than his rate coming down the hill. If it takes him 6 hours to climb the hill and 45 minutes to come down the hill, what is his rate coming down?

• Math: Algebra -

the distance is the same

Let s be his uphill speed

d/s = 6
d/(s+2.5) = .75

6s = .75(s+2.5)
6s = 3s/4 + 15/8
48s = 6s + 15
42s = 15
s = 15/42 = 5/14

So, he can go up at 5/14 mph and come down at 20/7 mph

6*5/14 = 30/14
3/4 * 20/7 = 60/28 = 30/14

Looks like the hill is 15/7 miles long.

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